1) The areas that should be caulked are horizontal and vertical seams along your shower door if you have one. Along the outside base of your tub and along edge of your tile by using a “tub and tile caulk like Kwik Seal Tub & Tile Adhesive Caulk which dries in 15 minutes is mildew resistant and if needed is also paintable.
2) For your corners which are already grouted, you will have to remove all grout with a grout saw or other tool in order to apply your caulk.
3) The way to make your caulking job look nice is to use painters tape by applying one peace above the gap and another below the gap on tub with a space between 3/8’’ – ¼’’ apart and apply the caulking into gap and then spread the caulk with a wet finger to get a nice even line. When this is complete, remove the tape immediately and you will have a nice professional looking caulk line.